Background: Strong evidence indicates physical activity (PA) reduces risk of bladder, breast, colon, endometrium, esophagus, gastric, and renal cancer, and there is moderate evidence for lung cancer. Individuals aged 40+ who are inactive are at high risk of developing cancers 58,65 but only 1/3 meet guidelines for PA;5-15 thus, they are an important group to target. While effective PA interventions exist, interventions often work only for some individuals or only for a limited time,16-18 thus establishing the need for interventions that can account for dynamic, idiosyncratic PA determinants in order to support each person?s PA. In response, we developed JustWalk, a modular adaptive mobile health (mHealth) intervention that makes daily N-of-1 adjustments to support PA for each person. JustWalk is based on Social Cognitive Theory (SCT) with N-of-1 adaptation driven by a mathematical dynamical model of SCT, which we have developed and validated. JustWalk can perform N-of-1 adaptation based on our innovative use of control engineering methods, which we call a control optimization trial (COT). We have a digital platform and empirical justification for our next step: to evaluate, in a randomized controlled trial (RCT), whether using a COT approach to continuously optimize a PA intervention to each individual is superior to an intervention that is identical but lacks the COT methods. Primary purpose: Evaluate differences in minutes/week of moderate-to-vigorous intensity PA (MVPA) among the COT- optimized vs. non-COT groups at 12 months. Hypotheses: We hypothesize significantly higher minutes/week of MVPA in the intervention arm (COT) relative to control (non-COT) as measured via ActiGraph (powered for effect size of ?0.32). Methods: We will conduct this RCT with 386 adults aged 40+ who are inactive and overweight/obesity. This is a high-risk group who would benefit from a PA intervention for cancer prevention and who would benefit from an adaptive intervention because of the idiosyncratic and dynamic nature of PA that is pronounced within this group. Assessments will be conducted at baseline, 6, and 12-months using a hip-worn ActiGraph for assessing minutes/week of MVPA, as justified by guidelines. Implications: This research is highly significant because our intervention would be the first scalable PA intervention squarely grounded in SCT with N-of-1 adaptation driven by a mathematical dynamical model version of SCT. Further, favorable results would justify use of our COT methods for other complex and highly idiosyncratic and dynamic behaviors such as weight management, smoking, or substance abuse. Finally, our work should improve understanding of engagement with digital health tools. This research is highly innovative as we would be the first to conduct a COT and to empirically evaluate its utility in an RCT.